I have to find someone to _____ my dog while I am on my business trip.

look after 是動詞片語，意為「照顧、照料、看管」，可接受詞，常用於人、兒童、寵物或物品。題幹的 find someone to look after my dog，正是「找人照顧我的狗」；符合目前官方答案。